It's kludgy, but you could always use ITA Matrix to search for flights from your home airport to anywhere Spirit flies. The Spirit timetable should make it fairly easy to get a list of airport codes for this purpose. You can also specify the airline you want under "Advanced Routing Codes"; in this case, you would enter
NK, which is Spirit's carrier code.
For example, if your home airport is Boston, you could consult the timetable to find that there are Spirit flights from BOS to ATL, DFW, FLL, RSW, LAS, MYR, and PBI. Searching for round-trips with departure
BOS and destination
ATL, DFW, FLL, RSW, LAS, MYR, PBI, with routing code
NK, yields the following results:
This is the search for a fixed date of departure & return, but you could equally well search for flights within a day or two of a given date, or search a range of dates using their "calendar of lowest fares" functionality.
This would become more tedious if your home airport is one of their "focus cities", with dozens of destinations; but it would still in principle be possible, and might be your best option if nobody comes up with a better one.